{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "## Q2利用math库计算圆的周长和面积"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "import statistics\n",
    "import matplotlib.pyplot as plt"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:22.171333Z",
     "end_time": "2024-07-04T21:56:22.683463Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "圆的周长： 12.566370614359172\n",
      "圆的面积： 12.566370614359172\n"
     ]
    }
   ],
   "source": [
    "r = 2\n",
    "print(\"圆的周长：\", 2 * math.pi * r)\n",
    "print(\"圆的面积：\", math.pi * r ** 2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:22.685456Z",
     "end_time": "2024-07-04T21:56:22.699194Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Q3 利用math库绘制$f(x)=exp(x)$函数图像，$x$的范围为$[-3,3]$"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_start = -3\n",
    "x_end = 3\n",
    "x_array = [x_start + i for i in range((x_end - x_start + 1))]\n",
    "y_array = [math.exp(x_idx) for x_idx in x_array]\n",
    "plt.plot(x_array, y_array, marker='.',\n",
    "         markersize=8,\n",
    "         markerfacecolor=\"w\",\n",
    "         markeredgecolor='k')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:22.701186Z",
     "end_time": "2024-07-04T21:56:22.827907Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Q4 利用math库计算并绘制$f(x)=exp(-x^2)$函数图像，$x$的范围为$[-3,3]$"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_start = -3\n",
    "x_end = 3\n",
    "x_array = [x_start + i for i in range((x_end - x_start + 1))]\n",
    "y_array = [math.exp(-x_idx ** 2) for x_idx in x_array]\n",
    "plt.plot(x_array, y_array, marker='.',\n",
    "         markersize=8,\n",
    "         markerfacecolor=\"w\",\n",
    "         markeredgecolor='k')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:22.825553Z",
     "end_time": "2024-07-04T21:56:22.932256Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Q5 利用random和statistics库完成如下实验。抛一枚质地均匀六面色子1000次，色子点数为[1,2,3,4,5,6]。可视化结均值随抛掷次数的变化。"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_flips = 1000\n",
    "results = [random.choices([1, 2, 3, 4, 5, 6])[0]\n",
    "           for _ in range(num_flips)]\n",
    "running_means = [statistics.mean(results[0:idx + 1])\n",
    "                 for idx in range(num_flips)]\n",
    "plt.plot(range(1, num_flips + 1), running_means)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:22.933253Z",
     "end_time": "2024-07-04T21:56:23.150624Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Q6 利用random和statistics库完成如下实验。抛一枚质地均匀六面色子1000次，色子点数为[1,2,3,4,5,6]对应的概率分别为[0.2,0.16,0.16,0.16,0.16,0.16]。可视化结均值随抛掷次数的变化。"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_flips = 1000\n",
    "results = [random.choices([1, 2, 3, 4, 5, 6], [0.2, 0.16, 0.16, 0.16, 0.16, 0.16])[0]\n",
    "           for _ in range(num_flips)]\n",
    "running_means = [statistics.mean(results[0:idx + 1])\n",
    "                 for idx in range(num_flips)]\n",
    "plt.plot(range(1, num_flips + 1), running_means)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-07-04T21:56:23.153196Z",
     "end_time": "2024-07-04T21:56:23.368492Z"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
